Comparative study of singularly perturbed two-point BVPs via: Fitted-mesh finite difference method, B-spline collocation method and finite element method

The objective of this paper is to present a comparative study of fitted-mesh finite difference method, B-spline collocation method and finite element method for general singularly perturbed two-point boundary value problems. Due to the small parameter ε{lunate}, the boundary layer arises. We have taken a piecewise-uniform fitted-mesh to resolve the boundary layer and we have shown that fitted-mesh finite difference method has ε{lunate}-uniform first order convergence, B-spline collocation method has almost second order ε{lunate}-uniform convergence and Ritz-Galerkin method also has almost second order ε{lunate}-uniform convergence. Two test examples have been solved to compare the maximum absolute error and rate of convergence of the methods.